Distributed Quantum Computing with Fan-Out Operations and Qudits: the Case of Distributed Global Gates (a Preliminary Study)

TL;DR

This work tackles distributing multipartite entanglement and global gates in quantum networks by leveraging one-shot GHZ-based fan-out and qudit-based circuit compression. It argues that GHZ-enabled fan-out can reduce circuit depth and entanglement overhead for distributed GMS/GCZ gates compared with naive bipartite approaches, and shows how encoding qubits into qudits further lowers inter-node resource needs. The authors provide concrete schemes for two- and three-node deployments, including dCNOT- and CSUM-based constructions, and quantify resource trade-offs across architectures. Together, these results inform compiler design and quantum data center planning toward more depth-efficient distributed quantum computation.

Abstract

Much recent work on distributed quantum computing have focused on the use of entangled pairs and distributed two qubit gates. But there has also been work on efficient schemes for achieving multipartite entanglement between nodes in a single shot, removing the need to generate multipartite entangled states using many entangled pairs. This paper looks at how multipartite entanglement resources (e.g., GHZ states) can be useful for distributed fan-out operations; we also consider the use of qudits of dimension four for distributed quantum circuit compression. In particular, we consider how such fan-out operations and qudits can be used to implement circuits which are challenging for distributed quantum computation, involving pairwise qubit interactions, i.e., what has been called global gates (a.k.a. global Mølmer-Sørensen gates). Such gates have been explored to possibly yield more efficient computations via reduced circuit depth, and can be carried out efficiently in some types of quantum hardware (e.g., trapped-ion quantum computers); we consider this as an exploration of an ``extreme'' case for distribution given the global qubit-qubit interactions. We also conclude with some implications for future work on quantum circuit compilation and quantum data centre design.

Figures (10)

• Figure 1: Distributed control-$U$ (i.e., dCNOT is when U=$X$ ($\oplus$) as shown) between nodes $QC$ and $QC'$ (the computation qubits are $c$, the control qubit, and $t$, the target qubit), and the wavy line illustrates a Bell pair involving the communication qubits from the two nodes both initially $\ket{0}$.
• Figure 2: Distributed multitarget control operation with single control qubit (on $A$) for multiple target qubits (one on $A$, one on $B$ and one on $C$)
• Figure 3: Distributed multitarget control operation with single control qubit (on $A'$) for multiple target qubits (one on $A$, one on $B$ and one on $C$) - all target qubits on different nodes from the control qubit.
• Figure 4: A $GMS_{1,2,3,4}$ gate marked with triangles (fan-out 1 and fan-out 2) and box ( dLMS 3) highlighting the qubits involved in a GHZ state for each triangle and a distributed control-U between qubits 3 and 4, which would be needed if the qubits were located on different nodes, one qubit per node.
• Figure 5: The first three LMS operations in the $GMS_{1,2,3,4}$ gate showing that a fan-out operation can be used for the single qubit control for $R_Z(-2\theta)$ in three different target qubits - the simplification is due to $HH=I$.